Since Beck made the first conjecture of this type, combinatorial identities on the excess between the number of parts in all partitions arising from a partition identity like Euler's are now fairly commonly referred to as “Beck-type identities." In recent past, a number of other interesting
Beck-type companions to other important identities have been established – see, e.g., [1]}, [2]}, [3]}, [4]}, [5]}.
